Boy, but my head is still reeling from the equation .....
Side comment - it doesn't matter all that much, I guess, but you have more brackets, there, than you can poke a stick at. If you want to play with equations, consider making them as simple as reasonably feasible ? Brackets can foul up arithmetic calculations really quickly if you don't nit pick along the way when you set the equation up.
Most folks who know me, know that I detest long equations if I can run the sums other (simpler) ways -
(a) long equations make it very easy to make mistakes and even harder to spot them most of the time. Those of us with any computer programming background know just what a curse coding equations and debugging the inevitable errors is ..
(b) if you can break the calculation up into stages, especially with a picture or two along the way ... makes things much easier for dumbos like me.
So, when I have a look at your equation, a couple of things jump out at me -
(a) if I run your equation, as it is, I get an answer which, probably, is not what you intended - indeed, a long way from what you intended ? Perhaps you might revisit your equation and see if you have made an error with brackets along the way ? When I make the pertinent correction, the answer is far more reasonable and agrees with your answer - still wrong, though.
(b) if I have a second look at the temperature deviation correction component I am wondering if you might have another look at the numbers and consider what the pressure height (from which you are figuring the temperature correction) might be ? A good point for why the odd picture and running calculation elements sequentially helps the brain figure out what's going on. Again, when I make the pertinent correction, the answer is even a bit more reasonable.
Once you have done both the above suggested corrections, you probably might find yourself closer to the question's preferred answer ?
Keep in mind that -
(a) 120 ft/deg is only an approximation anyway
(b) the usual calculations run the atmospherics as being dry which imposes yet another error - the usual pilot calculation being run here ignores humidity.
(c) if you use the ISA calculation equation, things get more complicated along the way - fortunately, we don't go to those sort of extremes so we don't get too much brain strain.
